(\partial)/(\partial y)((x-4)ln(xy))

解

\frac{\partial}{\partial y} ((x - 4) ln (x y))

\frac{x - 4}{y}

解答ステップ

\frac{\partial}{\partial y} ((x - 4) ln (x y))

x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= (x - 4) \frac{\partial}{\partial y} (ln (x y))

連鎖法則を適用:

\frac{1}{x y} \frac{\partial}{\partial y} (x y)

= \frac{1}{x y} \frac{\partial}{\partial y} (x y)

\frac{\partial}{\partial y} (x y) = x

= (x - 4) \frac{1}{x y} x

簡素化

(x - 4) \frac{1}{x y} x : \frac{x - 4}{y}

= \frac{x - 4}{y}